Abstract: Scheduling with deteriorating jobs has received increasing attention in recent years. Moreover, the machines are assumed to have unlimited intermediate buffers. In this paper, we study the two-machine deteriorating jobs flowshop problem with blocking where the objective is to minimize the makespan. A branch-and-bound algorithm incorporating with several dominance rules and a lower bound is provided to derive the optimal solution. In addition, several heuristic algorithms are also developed for near-optimal solution. Finally, a computational experiment is conducted to evaluate the performance of the proposed algorithms.